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On the maxima of suprema of dependent Gaussian models

Author

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  • Lanpeng Ji

    (University of Leeds)

  • Xiaofan Peng

    (University of Electronic Science and Technology of China)

Abstract

In this paper, we study the asymptotic distribution of the maxima of suprema of dependent Gaussian processes with trend. For different scales of the time horizon we obtain different normalizing functions for the convergence of the maxima. The obtained results not only have potential applications in estimating the delay of certain Gaussian fork-join queueing systems but also provide interesting insights to the extreme value theory for triangular arrays of random variables with row-wise dependence.

Suggested Citation

  • Lanpeng Ji & Xiaofan Peng, 2023. "On the maxima of suprema of dependent Gaussian models," Queueing Systems: Theory and Applications, Springer, vol. 105(1), pages 99-128, October.
    • Handle: RePEc:spr:queues:v:105:y:2023:i:1:d:10.1007_s11134-023-09880-0
    DOI: 10.1007/s11134-023-09880-0
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    References listed on IDEAS

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    1. Dieker, A.B., 2005. "Extremes of Gaussian processes over an infinite horizon," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 207-248, February.
    2. Ekaterina Morozova & Vladimir Panov, 2021. "Extreme Value Analysis for Mixture Models with Heavy-Tailed Impurity," Mathematics, MDPI, vol. 9(18), pages 1-24, September.
    3. Ji, Lanpeng & Peng, Xiaofan, 2023. "Extreme value theory for a sequence of suprema of a class of Gaussian processes with trend," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 418-452.
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